Polynomial with known root tangent squared

Geometry Level 5

\[ x^4 - ax^3 + bx^2 - cx + 1 \]

You are given that the polynomial above has a root of \( \tan^2\left(\frac{2\pi}{15}\right) \) for positive integers \(a,b\) and \(c\). Find the value of \(a + b + c\).


This question is from the set polynomial with known trigo root.

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